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arXiv · 1408.4381

Essential Normality of automorphic composition operators

Liangying Jiang·Caiheng Ouyang·Ruhan Zhao
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Abstract

We first characterize those composition operators that are essentially normal on the weighted Bergman space $A^2_s(D)$ for any real $s>-1$, where induced symbols are automorphisms of the unit disk $D$. Using the same technique, we investigate the automorphic composition operators on the Hardy space $H^2(B_N)$ and the weighted Bergman spaces $A^2_s(B_N)$ ($s>-1$). Furthermore, we give some composition operators induced by linear fractional self-maps of the unit ball $B_N$ that are not essentially normal.

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Liangying Jiang, Caiheng Ouyang, Ruhan Zhao. 2014-08-19. Essential Normality of automorphic composition operators. https://arxiv.org/abs/1408.4381

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